Application of the Monte Carlo Method to Heat Transfer in a Rarefied Gas

Abstract

A Monte Carlo method was developed and applied to the heat transfer between two parallel walls in a rarefied gas, using the IBM 709 computer. Three solutions were obtained, all at a temperature ratio between the walls of 4:1. One was for hard-sphere molecules at a Knudsen number of 2.0, and two were for Maxwellian molecules at Knudsen numbers of 0.53 and 1.64. These results appear to be of sufficient accuracy to differentiate between some of the approximate analytical methods available at present. It is believed that solutions could be obtained to any degree of accuracy, given sufficient time on a high-speed computer.